Brief snapshot of solution» Understand system functionality and get available technical details

» Define reference system for measurement of linear and rotational displacements in inertial frame

of reference

» At any instant‘t’, define the state of system and draw free body diagram of its individual systems.

» By applying Newton’s laws for translation and rotational motion, write force and torque balance

equations.

» Reassemble these force and torque balance equations for calculation of desired variables of

interest.

» Model these equations in Matlab-simulink (most preferable) or Easy5 or Amesim environment

for different systems and sub-systems.

» Model linear actuator system using available transfer function b/w voltage as input and actuation

Force as output. Integrate different subsystems and system to form plant model for complete

system. Provide Linear actuator Voltage as input to plant model and Primary and secondary

displacement as plant model’s Output with ‘C1’ & ‘C2’wheel displacement.

» Model system in simulink to calculate error between a desired primary displacement and plant

model’s calculated primary displacement. Model PI controller and connect it across plant model

with primary displacement as model output and regulated voltage as Input to plant model.

» Check secondary output of model whether it is in range or out of bounds. Below are different

options to minimize secondary displacements :

Open loop system: Carry out sensitivity analysis by varying design variables & Inputs to

the system within their tolerance band by creating different sets using crystal ball. After

carrying out this analysis, it will be clear which variables are positively or negatively

impacting the secondary displacement and how much system is sensitive by their impact.

Thereafter a sensible decision can be taken with available geometrical, practical and cost

constraints to minimize the secondary displacement.

Closed Loop system: Tune controller gains to minimize secondary displacement in

closed loop system.

Dimensioning

Where,

KCi,X : Transverse Spring constant in X-Direction for Ci (i=1,2) Spring KCi,Z : Longitudinal Spring constant in Z-Direction for Ci (i=1,2) Springli : Distance between specified sectionh : Height of Accuracy point from horizontal axis passing through CG

Define Reference ‘X’ & ‘Z’ axis

l1 l2 l3

hCGKC1,X ,

KC1,Z

KC2,X ,KC

2,Z

Assumptions

Wheels are assumed as rigid and are sliding on surface Transfer function b/w input voltage and force output is known for linear actuator All other dimensions and material properties are provided for calculation of mass , Centre of

gravity etc. Springs are considered linear.

Software’s to be used

Plant modeling & Controls (Any of below soft ware’s)

Matlab-simulink Amesim Easy5

Miscellaneous

Crystal Ball for data set generation Ms excel for steady state calculations Ms power point for report generation

System dynamics state at instant‘t’

Note: All the displacements shown above are measured from initial position. For example: XC1 & XC2

is the relative displacement of wheels measured wrt the initial position of the wheel. For simplification it is shown in above figure from reference axis

System 1: Free body diagram

System 1: Force and Moment Equations

Φ

Z1 Z3Z

X1X2

XC1 XC2

X

Z2

X3

FActuator

)sin(*1,1 lZK zc )sin(*2,2 lZK zc

)(1*22,2 CoslXXK Cxc

)(1*11,1 CoslXXK Cxc

System 2: Free body diagram

System 2: Force Equations

sin*sin*

)cos(1*)cos(1*

2,21,1

22,211,1

lZKlZKZm

FlXXKlXXKXm

zczc

ActuatorCxcCxc

By applying Newton’s second law for translation motion, we get

Moment equation for system can be written as

)sin()cos(1*)(sin*

)(sin*)sin()cos(1

111,111,1

22,2222,20

llXXKCosllZK

CosllZKllXXKJ

Cxczc

zcCxc

)sin()( 323 llZZKinematic relation to calculate secondary displacement of accuracy point

System 3: Linear actuatorSuppose transfer function for linear actuator is known between voltage and force it applies to given mechatronics system

Build plant model for subsystems

)sin(*

)sin(*

)cos(1*

)cos(1*

2,22,Re

1,11,Re

2,22,222

1,11,111

lZKN

lZKN

FlXXKXm

FlXXKXm

zcCactionGround

zcCactionGround

CFrictionCxCCC

CFrictionCxCCC

By applying Newton’s second law for translation motion, we get

0X If , )cos(1*

0X If ,

0X If , )cos(1*

0X If ,

C222,2

c22,Re 2,

C111,1

c11,Re 1,

lXXK

NF

lXXK

NF

CxC

CactionGroundCFriction

CxC

CactionGroundCFriction

G( s )=F Actuator (s )V Voltage(s )

Integrate sub-systems to form plant model of mechatronics system

System 3ActuatorF

VoltageV

Sensitivity analysis

Use crystal ball to generate set of inputs by using upper and lower tolerance band of design variables and Input sets with specified distribution

Record the Models output (Secondary Displacement at accuracy Point) for complete set of inputs and design variables.

Examine which few critical factors (Inputs and design variables) in your analysis cause the predominance of variation in the response variable of interest ( Secondary Displacement at accuracy Point )

Tune your design variables sensibly by analyzing below curves